Labour MP Diane Abbott has urged shadow chancellor Ed Balls to rethink his so-called mansion tax policy, warning that the “tax on London” will fail to raise enough to support the NHS as promised.

“I am worried about how much this policy will actually raise and I am worried about it as a sustainable funding source for the NHS,” the MP for Hackney told City A.M.

Homeowners in properties worth above £3m could be hit with annual tax bills averaging more than £10,000, the Institute for Fiscal Studies said this week.

But Abbott – who has been touted as a possible candidate in the battle to be London’s next mayor – said she feared wealthy London homeowners would find ways to avoid the tax if the amount they were asked to pay was too high. Other Labour MPs in the capital also remain sceptical, with Dame Tessa Jowell suggesting the party may need to look again at the figure it aims to raise through the tax. Balls has pledged that homeowners who are asset rich and income poor would only pay when they sell their homes.

“The mansion tax will have a dysfunctional effect in London due to the dysfunctional housing market here. The fair thing would be to look again at council tax, but nobody wants to do that, it would be politically very difficult,” Abbott said.

MPs such as Jowell continue to question the fairness of the tax. The Dulwich and West Norwood MP told City A.M. last night: “Eighty per cent of income from the mansion tax will be raised in London, but it will be spent nationally.”

Labour plans to raise £1.2bn from the tax, and has said the money will fund investment in the NHS. The plan depends on creating a system of property bands and asking homeowners to self-assess the worth of their house.

Those in homes between £2m and £3m will pay £3,000 a year, Balls announced earlier this week.

He has yet to set out how bands above £3m will work, but research from the IFS suggests people could be asked to stump up over £10,000 per year, and likely much more, if Labour is to raise the money it needs to satisfy its intended budget for the NHS.